Measures of concordance determined by $D_4$-invariant measures on $(0,1)^2$
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- by H. H. Edwards, P. Mikusiński and M. D. Taylor PDF
- Proc. Amer. Math. Soc. 133 (2005), 1505-1513 Request permission
Abstract:
A measure, $\mu$, on $(0,1)^2$ is said to be $D_4$-invariant if its value for any Borel set is invariant with respect to the symmetries of the unit square. A function, $\kappa$, generated in a certain way by a measure, $\mu$, on $(0,1)^2$ is shown to be a measure of concordance if and only if the generating measure is positive, regular, $D_4$-invariant, and satisfies certain inequalities. The construction examined here includes Blomqvist’s beta as a special case.References
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Additional Information
- H. H. Edwards
- Affiliation: Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, Florida 32816-1364
- Email: newcopulae@yahoo.com
- P. Mikusiński
- Affiliation: Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, Florida 32816-1364
- Email: piotrm@mail.ucf.edu
- M. D. Taylor
- Affiliation: Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, Florida 32816-1364
- Email: mtaylor@pegasus.cc.ucf.edu
- Received by editor(s): August 1, 2003
- Received by editor(s) in revised form: November 11, 2003, and January 13, 2004
- Published electronically: November 19, 2004
- Communicated by: Richard C. Bradley
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 1505-1513
- MSC (2000): Primary 62H05, 62H20
- DOI: https://doi.org/10.1090/S0002-9939-04-07641-5
- MathSciNet review: 2111952